# Finding acceleration only with known acceleration distance, final velocity, and mass for Newton's Third Law [closed]

So I have this problem that I am trying to figure out. I need to find the acceleration of a 4 kg object, that is accelerated through a distance of 1 m to the left to a final velocity of 6 m/s. This does not seem possible without knowing any times??

I know a = (vf-vi)/t
d = 0.5at^2
a = fnet/m

None of them seem to work with the given data.

It is the third law because a person on a frictionless surface throws the object to the left.

## closed as off-topic by ACuriousMind♦, Brandon Enright, Kyle Kanos, Rob Jeffries, Qmechanic♦Nov 23 '14 at 3:33

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• Was the object accelerated from rest? If so, you can set $v_0=0$ and solve the problem. – HDE 226868 Nov 22 '14 at 23:04
• yes it was accelerated from zero m/s – user65065 Nov 22 '14 at 23:06
• @HDE226868, but I still do not know the time. If I use s = d/t, then time is 1/6 s? – user65065 Nov 22 '14 at 23:09
• when I solve for time using Vf and t – user65065 Nov 22 '14 at 23:11

Here's what you do: You know $v_0$, $v_f$, and $x$. This means you can use the equation $$v_f^2=v_0^2+2ax$$ Re-arrange it to get $$a=\frac{v_f^2-v_0^2}{2x}$$ You also know the mass, $m$. You can use Newton' second law, $F=ma$, here: $$F=m\frac{v_f^2-v_0^2}{2x}$$ This should lead you to the answer.